A sustainable economic order quantity model with fuzzy inflation rate, fuzzy promotional effort and fuzzy deterioration rate

This study represent the exploration of an economic order quantity (EOQ) model where it is perceived that the cost at the starting time of an inventory and the estimated cost of an inventory are not necessarily the same. The reason is defined as a delay in the time interval between cost estimation. and the actual starting time of the inventory. Inflation of money, promotional strategies and debilitation rate of decaying items are included in the model. Instability in political ground or an uncertain situation of a country create more instability in the economic system. Thus, inflation of money is considered. The model represents deterioration rate, inflation of money, and promotional index in fuzzy sense for showing the parametric uncertainty. Therefore, the model is solved by the method of signed distance, triangular fuzzy, and trapezoidal fuzzy for maximization of profit. Carbon emissions due to transportation is calculated for adding the sustainability concept to the model. Optimal order quantity, optimal shortage quantity, optimal selling period and optimal shortage period are found to make the model distinctive. The formulated model is thoroughly explained for both crisp, triangular fuzzy, and trapezoidal fuzzy environment and it is concluded that the trapezoidal fuzzy number is better in its applicability for the decision makers. Because, under the trapezoidal fuzzy environment, the profit value is increased by 10.51% as compared to the crisp environment and 3.89% with respect to the triangular fuzzy environment. One more finding is that, trapezoidal fuzzy number is better with its simple arithmetic operation as well as its easy and intuitive interpretation approach. A practical example from a fertilizer company is considered in the model to add a real touch. Sensitivity analysis is performed and supported by graphical representation. Comparative analysis is derived to show the uniqueness of the model. The model ends with conclusions and direction to possible future studies.